Here is the full list of all 24 Blasting Agent: Ultimate Edition achievements.
Clear Level 2 on Hard Difficulty
Clear Level 1 on Hard Difficulty
Unlock the Yeti Costume
Clear Level 6 on Normal Difficulty
Unlock the Pule Bazooka Upgrade
Clear Level 5 on Normal Difficulty
Unlock the Repulsor Shield Upgrade
Clear Level 4 on Normal Difficulty
Unlock the Grav Jump Ability
Clear Level 3 on Normal Difficulty
Unlock the Frag Grenade Upgrade
Clear Level 2 on Normal Difficulty
Unlock the Spiked Boots Upgrade
Unlock the Ionic Dash Ability
Clear Level 1 on Normal Difficulty
Unlock the Ninja Costume
Unlock the Bearded Brother Costume
Unlock the Space Captain Costume
Unlock the Batty Guy Costume
Unlock the Polychromatic Suit Costume
Clear Level 3 on Hard Difficulty
Clear Level 4 on Hard Difficulty
Clear Level 5 on Hard Difficulty
Clear Level 6 on Hard Difficulty